Kate Winslet's Life Saved by Mildred Pierce Costar Guy Pearce

Guy Pearce is great to work with. In a pinch, he'll even save your life.

Kate Winslet found this out recently while filming Mildred Pierce for HBO. The period piece required Pearce, 43, to drive an unwieldy 1929 Cord automobile with heavy steering and awkward gears. And at one point, with Winslet, 35, in the passenger seat, they had a very close call.

"We'd finished a take, and a van came onto the road that we were on without seeing us," Pearce told PEOPLE at the miniseries' premiere this week in New York. "We both had to sort of swerve to get out of each other's way ... and I thought ... wow!"

Did he picture the headlines in the papers the next day? "Yeah, can you imagine?" he said.

Avoiding serious car accidents wasn't the only challenge on the set. Pearce and Winslet also had to film nude scenes together – for which both came prepared.

"I'm always pretty fit, generally," said Pearce, who also played the Duke of Windsor in The King's Speech. "It was about getting a body shape that was appropriate for that period, and not being too buffed. Having a tan was important, a real tan, but some of it was sprayed – in certain areas that don't normally see the sun."

Winslet, who wore Stella McCartney dress with a sheer side vent to the premiere, has shot nude scenes for several recent films, and thus brought plenty of experience to the set. "The most important thing is to have a sense of understanding and trust with one another, because it just makes it easier," she told PEOPLE.

And does she prepare physically – yoga, diet – before going wardrobe free? "No ... just me," she quipped.

Filming the miniseries, which begins airing Sunday on HBO, certainly brought the two actors close. Luckily, Pearce's wife is also named Kate – which might prove helpful in the long run.

"At least if I yell out 'Kate' in the middle of the night, then I'm okay," he joked, before adding: "My wife has as much of a crush on Kate as I do, so she was pleased for me."